conehate0712

2 years ago

The electrical resistance of a wire varies directly as the square of the diameter . if a wire 9.45m long and 0.09 cm in diameter has a resistance of a wire of the same material which is 15.5m in length and 0.16cm in diameter?

This is a standard direct variation problem. Such problems are encountered often in algebra, not just physics.
resistance varies directly as the square of the diameter MEANS
\(Resistance = k\cdot Diameter^{2}\)
We are given: wire 9.45m long and 0.09 cm in diameter has a resistance of a wire of the same material which is 15.5m in length and 0.16cm in diameter?
This is a little odd for two reasons:
1) the length is not important. Throw it out.
2) We have two partial hints and no complete hint.
Discarding the length will be more clear.
We are given: wire 0.09 cm in diameter has a resistance of a wire of the same material which is 0.16cm in diameter?
Thus: \(k\cdot (0.09\;cm)^{2} = k\cdot (0.16\;cm)^{2}\)
We see immediately that this is no good, since k = 0 is the only solution. I have to believe we DID need the length and the variation description provided is incorrect.
I would guess that it is this: The resistance of a wire varies directly with its length and inversely with the square of its diameter
Now, we can solve it with the original information given, Let's see what you get.
@conehate0712